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Frontiers of Mathematics in China

Front. Math. China    2017, Vol. 12 Issue (4) : 879-889     DOI: 10.1007/s11464-017-0622-7
RESEARCH ARTICLE |
Some q-inequalities for Hausdorff operators
Jiuhua GUO, Fayou ZHAO()
Department of Mathematics, Shanghai University, Shanghai 200444, China
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Abstract

We calculate the sharp bounds for some q-analysis variants of Hausdorff type inequalities of the form+0(+0ϕ(t)tfxtdqt)pdqxCϕb0fp(t)dqt.As applications, we obtain several sharp q-analysis inequalities of the classical positive integral operators, including the Hardy operator and its adjoint operator, the Hilbert operator, and the Hardy-Littlewood-Pólya operator.

Keywords Sharp constant      Hausdorff operator      Hilbert operator      q-inequality     
Corresponding Authors: Fayou ZHAO   
Issue Date: 06 July 2017
 Cite this article:   
Jiuhua GUO,Fayou ZHAO. Some q-inequalities for Hausdorff operators[J]. Front. Math. China, 2017, 12(4): 879-889.
 URL:  
http://journal.hep.com.cn/fmc/EN/10.1007/s11464-017-0622-7
http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/879
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Jiuhua GUO
Fayou ZHAO
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